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The online **Linear Equation Calculator** is a useful tool for solving linear equations of the form “ax + b = 0,” where a and b are constants and x is the variable.

The **Linear Equation Solver** is easy to use and is ideal for students learning how to solve linear equations or for anyone needing to quickly and easily solve linear equations.

To use the Linear Equations Calculator you must perform the following steps:

- Enter the linear equation. You can enter a linear equation with several unknown variables. Use only the functions and operators that are presented in Table 1.
- If you have entered a linear equation with multiple variables, select the variable for which you want to solve the equation.
- Press the “Calculate” button to get the solution explained step by step.

Valid functions and symbols | Description |
---|---|

sqrt() | Square root |

ln() | Natural logarithm |

log() | Logarithm base 10 |

^ | Exponents |

abs() | Absolute value |

sin(), cos(), tan(), csc(), sec(), cot() | Basic trigonometric functions |

asin(), acos(), atan(), acsc(), asec(), acot() | Inverse trigonometric functions |

sinh(), cosh(), tanh(), csch(), sech(), coth() | Hyperbolic functions |

asinh(), acosh(), atanh(), acsch(), asech(), acoth() | Inverse hyperbolic functions |

pi | PI number (π = 3.14159...) |

e | Neper number (e= 2.71828...) |

i | To indicate the imaginary component of a complex number. |

inf | ∞ |

Table 1: Valid functions and symbols

A linear equation is an equation in which the highest exponent of the variable is 1. They take the form of “ax + b = 0,” where a and b are constants and x is the variable.

For example, the equation “2x + 3 = 7” is a linear equation, because the highest exponent of x is 1. On the other hand, the equation “x^2 + 3x + 2 = 0” is not a linear equation, because the highest exponent of x is 2.

Linear equations are useful for modeling many real-world situations, such as calculating distances or determining the slope of a line. They are also relatively easy to solve, making them a common topic in algebra and pre-calculus courses.

To solve a linear equation, you can use one of several methods. The most common method is to isolate the variable by using inverse operations, such as addition and subtraction, to get the variable by itself on one side of the equation. For example, to solve the equation “2x + 3 = 7,” you would subtract 3 from both sides to get “2x = 4,” and then divide both sides by 2 to get the solution: “x = 2.”

Another method for solving linear equations is graphing. To graph a linear equation, you can plot points that satisfy the equation and then draw a line through those points. The intersection of the line with the x-axis (the y-intercept) represents the solution to the equation.

Linear equations are important in many fields because they describe simple and straightforward relationships between variables. Some common applications of linear equations include:

Modeling real-world situations: Linear equations can be used to model relationships between quantities in the real world. For example, you might use a linear equation to model the relationship between the number of products produced and the cost of production.

Optimization problems: Linear equations can be used to find the maximum or minimum values of a function, which is useful in many optimization problems.

Regression analysis: Linear equations can be used to fit a line to a set of data points and predict future values of a variable. This is useful in statistical analysis and data mining.